• Wind and Structures
• /
• v.29 no.3
• /
• pp.163-175
• /
• 2019

Multispan suspension bridges make a good alternative to single-span ones if the crossed strait or river width exceeds 2-3 km. However, multispan three-tower suspension bridges are found to be very sensitive to the wind load due to the lack of effective longitudinal constraint at their central tower. Moreover, at certain critical wind speed values, the aerostatic instability with sharply deteriorating dynamic characteristics may occur with catastrophic consequences. An attempt of an in-depth study on the aerostatic stability mode and damage mechanism of three-tower suspension bridges is made in this paper based on the assessment of strain energy and dynamic characteristics of three particular three-tower suspension bridges in China under different wind speeds and their further integration into the aerostatic stability analysis. The results obtained on the three bridges under study strongly suggest that their aerostatic instability mode is controlled by the coupled action of the anti-symmetric torsion and vertical bending of the two main-spans' deck, together with the longitudinal bending of the towers, which can be regarded as the first-order torsion vibration mode coupled with the first-order vertical bending vibration mode. The growth rates of the torsional and vertical bending strain energy of the deck after the aerostatic instability are higher than those of the lateral bending. The bending and torsion frequencies decrease rapidly when the wind speed approaches the critical value, while the frequencies of the anti-symmetric vibration modes drop more sharply than those of the symmetric ones. The obtained dependences between the critical wind speed, strain energy, and dynamic characteristics of the bridge components under the aerostatic instability modes are considered instrumental in strength and integrity calculation of three-tower suspension bridges.

• Structural Engineering and Mechanics
• /
• v.73 no.6
• /
• pp.641-649
• /
• 2020

The determination of midtower longitudinal stiffness has become an essential component in the preliminary design of multi-tower suspension bridges. For a specific multi-tower suspension bridge, the midtower longitudinal stiffness must be controlled within a certain range to meet the requirements of sliding resistance coefficient and deflection-to-span ratio. This study presents a numerical method to divide different types of midtower and determine rational range of longitudinal stiffness for rigid midtower. In this method, influence curves of midtower longitudinal stiffness on sliding resistance coefficient and maximum vertical deflection-to-span ratio are first obtained from the finite element analysis. Then, different types of midtower are divided based on the regression analysis of influence curves. Finally, rational range for longitudinal stiffness of rigid midtower is derived. The Oujiang River North Estuary Bridge which is a three-tower four-span suspension bridge with two main spans of 800m under construction in China is selected as the subject of this study. This will be the first three-tower four-span suspension bridge with steel truss girders and concrete midtower in the world. The proposed method provides an effective and feasible tool for engineers to design midtower of multi-tower suspension bridges.

• Wind and Structures
• /
• v.38 no.1
• /
• pp.43-58
• /
• 2024

To ensure the flutter stability of three-tower suspension bridges under skew wind, by using the computational procedure of 3D refined flutter analysis of long-span bridges under skew wind, in which structural nonlinearity, the static wind action(also known as the aerostatic effect) and the full-mode coupling effect etc., are fully considered, the flutter stability of a three-tower suspension bridge-the Taizhou Bridge over the Yangtze River in completion and during the deck erection is numerically investigated under the constant uniform skew wind, and the influences of skew wind and aerostatic effects on the flutter stability of the bridge under the service and construction conditions are assessed. The results show that the flutter critical wind speeds of three-tower suspension bridge under service and construction conditions fluctuate with the increase of wind yaw angle instead of a monotonous cosine rule as the decomposition method proposed, and reach the minimum mostly in the case of skew wind. Both the skew wind and aerostatic effects significantly reduce the flutter stability of three-tower suspension bridge under the service and construction conditions, and the combined skew wind and aerostatic effects further deteriorate the flutter stability. Both the skew wind and aerostatic effects do not change the evolution of flutter stability of the bridge during the deck erection, and compared to the service condition, they lead to a greater decrease of flutter critical wind speed of the bridge during deck erection, and the influence of the combined skew wind and aerostatic effects is more prominent. Therefore, the skew wind and aerostatic effects must be considered accurately in the flutter analysis of three-tower suspension bridges.

• Steel and Composite Structures
• /
• v.32 no.2
• /
• pp.189-198
• /
• 2019

This paper aims to study the mechanical performance of three-tower four-span suspension bridges with steel truss girders, including the static and dynamic characteristics of the bridge system, and more importantly, the influence of structural parameters including the side-main span ratio, sag-to-span ratio and the girder stiffness on key mechanical indices. For this purpose, the Oujiang River North Estuary Bridge which is a three-tower four-span suspension bridge with two main spans of 800m under construction in China is taken as an example in this study. This will be the first three-tower suspension bridge with steel truss girders in the world. The mechanical performance study and parametric analysis are conducted based on a validated three-dimensional spatial truss finite element model established for the Oujiang River North Estuary Bridge using MIDAS Civil. It is found that a relatively small side-main span ratio seems to be quite appropriate from the perspective of mechanical performance. And decreasing the sag-to-span ratio is an effective way to reduce the horizontal force subjected to the midtower and improve the antiskid safety of the main cable, while the vertical stiffness of the bridge will be reduced. However, the girder stiffness is shown to be of minimal significance on the mechanical performance. The findings from this paper can be used for design of three-tower suspension bridges with steel truss girders.

• Wind and Structures
• /
• v.38 no.6
• /
• pp.427-443
• /
• 2024

By using a computational program of three-dimensional aerostatic and aerodynamic stability analysis of long-span bridges under skew wind, the dynamic characteristics and structural stability(including the aerostatic and aerodynamic stability) of a three-tower cable-stayed-suspension hybrid bridge with main span of 1 400 meters are investigated numerically under skew wind, and the skew wind and aerostatic effects on the aerostatic and aerodynamic stability of three-tower cable-stayedsuspension hybrid bridge are ascertained. The results show that the three-tower cable-stayed-suspension hybrid bridge is a longspan structure with greater flexibility, and it is more susceptible to the wind action. The aerostatic instability of three-tower cable-stayed-suspension hybrid bridges is characterized by the coupling of vertical bending and torsion of the girder, and the skew wind does not affect the aerostatic instability mode. The skew wind has positive or negative effects on the aerostatic stability of the bridge, the influence is between -5.38% and 4.64%, and in most cases, it reduces the aerostatic stability of the bridge. With the increase of wind yaw angle, the critical wind speed of aerostatic instability does not vary as the cosine rule as proposed by the skew wind decomposition method, the skew wind decomposition method may overestimate the aerostatic stability, and the maximum overestimation is 16.7%. The flutter critical wind speed fluctuates with the increase of wind yaw angle, and it may reach to the minimum value under the skew wind. The skew wind has limited effect on the aerodynamic stability of three-tower cable-stayed-suspension hybrid bridge, however the aerostatic effect significantly reduces the aerodynamic stability of the bridge under skew wind, the reduction is between 3.66% and 21.86%, with an overall average drop of 11.59%. The combined effect of skew and static winds further reduces the critical flutter wind speed, the decrease is between 7.91% and 19.37%, with an overall average decrease of 11.85%. Therefore, the effects of skew and static winds must be comprehensively considered in the aerostatic and aerodynamic stability analysis of three-tower cable-stayed-suspension hybrid bridges.

• Structural Engineering and Mechanics
• /
• v.50 no.2
• /
• pp.215-229
• /
• 2014

Due to the lack of effective longitudinal constraint for center tower, structural stiffness of three-tower suspension bridge becomes less than that of two-tower suspension bridge, and therefore it becomes more susceptible to the seismic action. By taking a three-tower suspension bridge-the Taizhou Highway Bridge over the Yangtze River with two main spans of 1080 m as example, structural dynamic characteristics and seismic performance of the bridge is investigated, and the effects of cable's sag to span ratio, structural stiffness of the center tower, and longitudinal constraint of the girder on seismic response of the bridge are also investigated, and the favorable structural system is discussed with respect to seismic performance. The results show that structural response under lateral seismic action is more remarkable, especially for the side towers, and therefore more attentions should be paid to the lateral seismic performance and also the side towers. Large cable's sag, flexible center tower and the longitudinal elastic cable between the center tower and the girder are favorable to improve structural seismic performance of long-span three-tower suspension bridges.

• Wind and Structures
• /
• v.11 no.4
• /
• pp.341-344
• /
• 2008

• Structural Engineering and Mechanics
• /
• v.81 no.2
• /
• pp.147-161
• /
• 2022

The Brace-Type Shear Fuse (BSF) device is a newly proposed steel damper with excellent cumulative ductility and stable energy dissipation. In consideration of the current situation where there are not many alternatives for transversal seismic devices used in long-span three-tower self-anchored bridges (TSSBs), this paper implements improved BSFs into the world's longest TSSB, named Jinan Fenghuang Yellow River Bridge. The new details of the BSF are developed for the TSSB, and the force-displacement hysteretic curves of the BSFs are obtained using finite element (FE) simulations. A three-dimensional refined finite element model for the research TSSB was established in SAP2000, and the effects of BSFs on dynamic characteristics and seismic response of the TSSB under different site conditions were investigated by the numerical simulation method. The results show that remarkable controlling effects of BSFs on seismic response of TSSBs under different site conditions were obtained. Compared with the case without BSFs, the TSSB installed with BSFs has mitigation ratios of the tower top displacement, lateral girder displacement, tower bending moment and tower shear force exceeding 95%, 78%, 330% and 346%, respectively. Meanwhile, BSFs have a sufficient restoring force mechanism with a minor post-earthquake residual displacement. The proposed BSFs exhibit good application prospects in long-span TSSBs.

• Journal of Korean Society of Steel Construction
• /
• v.23 no.6
• /
• pp.669-677
• /
• 2011

The multi-span suspension bridge generally has more than three towers and two main spans. To economically and effectively design a multi-span suspension bridge, the proper stiffness ratio of the center tower to the side tower must be determined. This study was conducted to propose a method of figuring out briefly the structural behavior of the towers in a multi-span suspension bridge. In the equivalent suspension bridge model, the main cable of the multi-span suspension bridge is idealized as an equivalent cable spring, and the external loads of horizontal and vertical forces that were calculated using the tensile forces of the main cable were applied on top of the towers. The equilibrium equations of the equivalent multi-span suspension bridge model were derived and the equations were solved via nonlinear analysis. To verify the proposed method, a sample four-span suspension bridge with a main span length of 3,000 m was analyzed using thefinite element method. The displacements and moment reactions of each tower in the proposed method were compared with the FEM analysis results. Consequently, the results of the analysis of the equivalent suspension bridge model tended to be consistent with the results of the FEM analysis.

• Structural Engineering and Mechanics
• /
• v.80 no.6
• /
• pp.749-765
• /
• 2021

Suspension bridges bear large eccentric live loads in rush hours when most vehicles travel in one direction on the left or right side of the bridge. With the increasing number and weight of vehicles and the girder widening, the eccentric live load effect on the bridge behavior, including bending and distortion of the main girder, gets more pronounced, even jeopardizing bridge safety. This study proposes an analytical algorithm based on multi-catenary theory for predicting the suspension bridge responses to eccentric live load via the nonlinear generalized reduced gradient method. A set of governing equations is derived to solve the following unknown values: the girder rigid-body displacement in the longitudinal direction; the horizontal projection lengths of main cable's segments; the parameters of catenary equations and horizontal forces of the side span cable segments and the leftmost segments of middle span cables; the suspender tensions and the bearing reactions. Then girder's responses, including rigid-body displacement in the longitudinal direction, deflections, and torsion angles; suspenders' responses, including the suspender tensions and the hanging point displacements; main cables' responses, including the horizontal forces of each segment; and the longitudinal displacement of the pylons' tower top under eccentric load can be calculated. The response of an exemplar suspension bridge with three spans of 168, 548, and 168 m is calculated by the proposed analytical method and the finite element method in two eccentric live load cases, and their results prove the former's feasibility. The nonuniform distribution of the live load in the lateral direction is shown to impose a greater threat to suspension bridge safety than that in the longitudinal direction, while some other specific features revealed by the proposed method are discussed in detail.